An apparently innocent problem in Membrane Computing

The search for effcient solutions of computationally hard problems by means of families of membrane systems has lead to a wide and prosperous eld of research. The study of computational complexity theory in Membrane Computing is mainly based on the look for frontiers of effciency between different classes of membrane systems. Every frontier provides a powerful tool for tackling the P versus NP problem in the following way. Given two classes of recognizer membrane systems R1 and R2, being systems from R1 non-effcient (that is, capable of solving only problems from the class P) and systems from R2 presumably e cient (that is, capable of solving NP-complete problems), and R2 the same class that R1 with some ingredients added, passing from R1 to R2 is comparable to passing from the non effciency to the presumed effciency. In order to prove that P = NP, it would be enough to, given a solution of an NP-complete problem by means of a family of recognizer membrane systems from R2, try to remove the added ingredients to R2 from R1. In this paper, we study if it is possible to solve SAT by means of a family of recognizer P systems from AM0(�����d;+n), whose non-effciency was demonstrated already

Mutual Mobile Membranes with Timers

A feature of current membrane systems is the fact that objects and membranes are persistent. However, this is not true in the real world. In fact, cells and intracellular proteins have a well-defined lifetime. Inspired from these biological facts, we define a model of systems of mobile membranes in which each membrane and each object has a timer representing their lifetime. We show that systems of mutual mobile membranes with and without timers have the same computational power. An encoding of timed safe mobile ambients into systems of mutual mobile membranes with timers offers a relationship between two formalisms used in describing biological systems

Computing with cells: membrane systems - some complexity issues.

Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism

Brownian motion: a paradigm of soft matter and biological physics

This is a pedagogical introduction to Brownian motion on the occasion of the 100th anniversary of Einstein's 1905 paper on the subject. After briefly reviewing Einstein's work in its contemporary context, we pursue some lines of further developments and applications in soft condensed matter and biology. Over the last century Brownian motion became promoted from an odd curiosity of marginal scientific interest to a guiding theme pervading all of the modern (live) sciences.Comment: 30 pages, revie

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarising their densely packed and heterogeneous structures. The most familiar phenomenon is a power-law increase of the MSD, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations, non-gaussian distributions of the displacements, heterogeneous diffusion, and immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarise some widely used theoretical models: gaussian models like FBM and Langevin equations for visco-elastic media, the CTRW model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Emphasis is put on the spatio-temporal properties of the transport in terms of 2-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even for identical MSDs. Then, we review the theory underlying common experimental techniques in the presence of anomalous transport: single-particle tracking, FCS, and FRAP. We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where model systems mimic physiological crowding conditions. Finally, computer simulations play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.Comment: review article, to appear in Rep. Prog. Phy

Roadmap on semiconductor-cell biointerfaces.

This roadmap outlines the role semiconductor-based materials play in understanding the complex biophysical dynamics at multiple length scales, as well as the design and implementation of next-generation electronic, optoelectronic, and mechanical devices for biointerfaces. The roadmap emphasizes the advantages of semiconductor building blocks in interfacing, monitoring, and manipulating the activity of biological components, and discusses the possibility of using active semiconductor-cell interfaces for discovering new signaling processes in the biological world

First Steps Towards Linking Membrane Depth and the Polynomial Hierarchy

In this paper we take the first steps in studying possible connections between non-elementary division with limited membrane depth and the levels of the Polynomial Hierarchy. We present a uniform family with a membrane structure of depth d + 1 that solves a problem complete for level d of the Polynomial Hierarchy